In several significant computer typography systems, the notation for an en dash is a doubled hyphen (--), and for an em dash a tripled one (---). Notably LaTeX and Markdown (Pandoc flavoured: <https://pandoc.org/MANUAL.html>).
In LaTeX I’ve been using \textemdash instead. I don’t actually know why, just, usually these sort of longer names tend to have some niche edge case they handle better.
em-dashes and parenthetical should be used sparingly so it isn’t too annoying to do all the extra typing.
My preference is for spare markup where at all possible. Less typing, less mental overhead, clearer source text.
If it's necessary to be explicit for clarity and proper rendering, then sure. But otherwise, the less friction the better.
After years of procrastinating in learning LaTeX (the Lion Book turned out to be a clear, delightful, and highly useful reference), one of the pleasant surprises was that paragraphs are simply denoted by two carriage returns. After years of hand-coding HTML where matching <p> and </p> tags (among many others) was a constant occupational hazard, this was just ... pleasing.
Markdown has a similar philosophy, if a far more restricted set of capabilities. That set is however sufficient for a tremendous number documents, and if it's ultimately insufficient still remains a useful way to get started with writing.
I've been through enough different HTML variants whilst not having to adhere strictly to standards that I'm moderately fuzzy what the current state of the standard is. I hear the current standard is also ... large.[1]
But even if it's not strictly necessary to balance <p> tags ... it is necessary to do so with many other HTML elements, and missing or mis-typed tags can utterly bork a page, particularly if there's any complexity to it.
(Hand-crafting tends to minimise that complexity, but it's still possible to get reasonably twisted.)
That said, checking one of my favourite HTML5 references, whose page source itself is a beautiful example of clean HTML ... I see that Mark Pilgrim in fact omits the close tags on his paragraphs:
